Question

Известно, что m2+n2=1. Найдите m6+3m2n2+n6

Answer 1

$m^2+n^2=1 \\ (m^2+n^2)^3=1^3 \\ m^6+3m^4n^2 + 3m^2n^4 + n^6 = 1 \\ m^6 + n^6 + 3m^2n^2(m^2+n^2)=1 \\ m^6 +n^6 +3m^2n^2=1$
Ответ 1

Answer 2

m²+n²=1
(m²+n²)³=1³
m⁶+3m⁴n²+3m²n⁴+n⁶=1
m⁶+3m²n²*(m²+n²)+n⁶=1
m⁶+3m²n²*1+n⁶=1.
m⁶+3m²n²+n⁶=1.